Switzerland benefits from bilateral treaties that allow it free access to the European market

ZURICH—Switzerland’s swing to the right in its parliamentary election could put the Alpine country’s relations with the European Union under strain and weigh on long-term growth, economists say.

The success of the populist Swiss People’s Party, or SVP, could also trigger the exit of Eveline Widmer-Schlumpf, the head of Switzerland’s finance department who has overseen the dismantling of Swiss banking secrecy.